Probabilistic Reach-Avoid Reachability in Nondeterministic Systems with Time-VaryingTargets and Obstacles

The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A numerical method is proposed to compute probabilistic reachable sets. First, a scalar function in the state space is constructed by backward recursion and grid interpolation, and then the probability reachable set is represented as a nonzero level set of this scalar function. In addition, based on the constructed scalar function, the optimal control policy can be designed. At the end of this paper, some examples are taken to illustrate the validity and accuracy of the proposed method.